AE $225$ problem: A supersonic converging$-$diverging nozzle is near the exit of a

turbojet engine. Its cross$-$section is circular. The gas has the properties of air, and the

flow is isentropic$.$ At the throat location $($the minimum area$)$ the air flow is choked $($is

Mach one$)$ and the throat has diameter of $20$ cm $.$

a$)$ Downstream of the throat the area of the nozzle increases. At the nozzle exit the Mach

number is $2\mathrm{.}5.$ What is the nozzle diameter $($in cm $)$ at the exit?

b$)$ At the location where the nozzle diameter is $25$ cm $,$ what is the gas velocity?

c$)$ If the air has a stagnation pressure $(p_0)$ of $60$ atm and a stagnation temperature of $1200$

K upstream of the throat, what is the mass flow rate in $k\frac{g}{sec}?$ Hint: use Fliegner's

formula $($below$)$ that is on p$.71$ of our textbook by Hill and Peterson.

$m_2^{}=[0\mathrm{.}040(\frac{kg}{s})P{a}^{-1}{m}^{-2}{K}^{\frac{1}{2}}],([p_{02},A_2])(T_{02}{)}^{-\frac{1}{2}}$

Location $"2"$ is any location, since the mass $/$ sec is the same at all streamwise x $-$

locations. Note: $p_0,T_0$ and $A^{*}$ are the same values at all x $-$locations.